EXCHANGE 


SPECTRAL   PHOTOMETRIC 
STUDIES 


-  BY  — 


DANIEL  WILLIAM  MURPHY 


A  THESIS 

PRESENTED  TO  THE  FACULTY  OF  LELAND  STANFORD  JUNIOR  UNIVERSITY 
FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


MAY,  1896 


THE 

ASTROPHYSICAL    JOURNAL 

AN    INTERNATIONAL    REVIEW    OF    SPECTROSCOPY 
AND    ASTRONOMICAL    PHYSICS 


JUNE 


VOLUME vi  j  LJ  i>  L     iw/  NUMBER  i 


SPECTRAL  PHOTOMETRIC  STUDIES. 

By    D.  W.  MURPHY. 

DETERMINATION  BY  MEANS  OF  THE  ROTATING  SECTOR  OF  THE  RELA- 
TION OF  SPECTRUM  INTENSITY  TO  THE  WIDTH  OF  THE  COL- 
LIMATOR  SLIT. 

AMONG  the  different  methods  of  comparing  the  intensities  of 
two  spectra  that  of  Vicrordt  is  the  most  common.  The  instru- 
ment used,  in  its  simplest  form,  differs  from  the  ordinary  spec- 
trometer only  in  the  arrangement  of  the  collimator  slit.  When 
the  apparatus  is  to  be  used  for  photometric  purposes  the  col 
limator  slit  is  replaced  by  two  separate  slits  located  one  directly 
above  the  other.  The  width  of  each  slit  is  measured  by  means 
of  a  micrometer  screw,  and  each  in  turn  may  be  lighted  from 
either  of  the  sources  whose  intensities  arc  to  be  compared.1 
The  spectra  thus  formed  are  situated  one  above  the  other,  and 
are  separated  by  a  narrow  dark  band. 

The  observations  are  made  by  means  of  an  ocular  which, 
being  supplied  with  an  adjustable  slit,  allows  all  the  spectrum  to 
be  cut  off  except  that  part  in  which  the  comparisons  are  to  be 
made.  The  two  fields  are  brought  to  the  same  intensities  by 
varying  the  widths  of  the  two  parts  of  the  double  collimator 

1  When  measuring  the  amount  of  absorption  both  spectra  are  lighted  from  the 
same  source,  and  the  absorption  medium  is  placed  between  the  light  and  one  of  the 
slits. 


239402 


2  /).  ir. 

slit.  From  the  relations  of  the  slit  widths  for  equal  intensities 
in  the  different  parts  of  the  spectrum,  the  intensity  for  different 
colors  is  found.  According  to  Vierordt  we  assume  that  the 
intensity  of  a  spectrum  so  lighted  is  directly  proportional  to  the 
width  of  the  collimator  slit.  When  the  two  spectra  are  of  the 
same  intensity  the  lights  are  inversely  proportional  to  their 
respective  slit  widths. 

We  shall  investigate  under  what  conditions  this  principle 
introduced  by  Vierordt  is  correct,  both  for  unilateral  and  for 
bilateral  slits.  We  know  for  both  cases  that  when  the  width  of 
the  slit  is  doubled,  twice  the  amount  of  light  comes  to  the  field 
of  the  observer. 

The  question  which  we  are  then  called  upon  to  solve  is,  does 
the  doubling  of  the  amount  of  light  in  this  manner  double  the 
intensity  of  every  part  of  the  spectrum  ? 

Let  us  imagine,  first,  an  infinitely  narrow  slit ;  the  spectrum 
from  such  a  source  may  be  called  a  pure  spectrum,  since  any 
point  in  it  will  contain  light  of  but  one  wave-length.  If  this  slit 
be  moved  in  a  direction  perpendicular  to  the  edge  of  the  prism 
the  spectrum  will  travel  in  the  same  direction  ;  and  a  stationary 
point,  as  the  light  traveled  over  it,  would  be  illuminated  by  light 
of  different  colors.  Next,  let  us  consider  a  wide  slit,  and  think 
of  its  being  divided  into  infinitely  narrow  ones ;  we  recognize 
that  every  part  of  the  spectrum  from  such  a  source  will  consist 
of  lights  of  different  wave-lengths  superposed  upon  each  other. 
Such  a  spectrum  we  will  call  an  impure  one,  and  it  is  with  such 
that  we  are  required  to  deal  in  practical  measurements. 

With  a  unilateral  slit  only  waves  that  are  either  greater  or 
less,  depending  upon  the  direction  of  the  opening  of  the  slit, 
than  the  fundamental  wave,  will  be  superposed  upon  it.  If  a 
bilateral  slit  is  used  the  extra  waves  which  are  brought  to  a  given 
point,  due  to  the  opening  of  the  slit,  will  be  both  greater  and 
less  than  the  fundamental  wave. 

From  the  above  consideration  it  follows:  that  with  a  uni- 
lateral slit  the  law  of  proportionality  holds  only  when  the  inten- 
sities of  the  adjacent  parts  of  the  spectrum  arc  the  same ;  or, 


SPECTRAL  PHOTOMETRIC  STUDIES  3 

where  the  curve  of  intensity  is  parallel  to  the  one  axis  of 
coordinates.  With  the  bilateral  slit  the  law  holds  where  the 
curve  of  intensity  is  a  straight  line,  and  may  be  true  for  other 
curves  in  the  region  of  inflection  points.  In  the  latter  case  the 
differentials  of  the  increase  in  intensities  due  to  the  light  from 
the  opposite  sides  of  the  slit,  must  be  equal  and  of  opposite 
signs. 

According  to  the  measurements  of  Fraunhofer,  Koenig, 
Brodhun  and  others,  the  distribution  of  intensity  in  the  spectrum 
of  the  Sun  and  other  incandescent  bodies  corresponds  approx- 
imately to  the  curve  shown  in  Fig.  I. 


FIG.  i. 

The  abscissae  represent  the  wave-lengths,  and  the  ordinates 
the  corresponding  intensities.  From  this  curve  it  follows  that 
the  unilateral  slit  is  to  be  used  only  in  those  parts  of  the  spec- 
trum where  the  curve  of  intensity  is  parallel  to  the  axis.  This 
is  true  for  only  a  small  part  of  the  spectrum  in  the  region  cd.  The 
bilateral  slit,  on  the  other  hand,  will  give  true  results  not  only  at 
cd,  but  in  the  vicinity  of  the  two  points  b  and  e.  When  the 
curve  is  convex  to  the  axis,  as  at  ab  and  ef,  the  increase  in  inten- 
sity must  be  more  rapid  than  the  increase  in  the  slit  width.  If 
the  curve  is  concave  to  the  axis,  as  at  bet  the  increase  in  intensity 
is  less  rapid  than  that  of  the  slit  width. 

In  order  to  prove  the  correctness  of  these  inferences,  and 
to  determine  the  magnitude  of  the  deviation  from  the  law  of 
proportionality,  the  following  observations  were  made. 

Method  of  observation  and  apparatus  used. — The  photometer 
measurements  were  made  with  the  Lummer-Brodhun  spectral 


/>.   //'.  MURPHY 


photometer,  a  complete  cleseription  of  which  may  be  found  in 
the  Zcitsclirift  fiir  Instntmentenkunde  for  April  1892.  This  instru- 
ment differs  in  two  respects  from  the  spectrometers  of  Vicrordt 
and  others.  First,  it  is  supplied  with  two  collimator  tubes,  C 
and  C ',  placed  perpendicular  to  each  other  (sec  Fig.  2);  and, 
second,  the  observations  are  made,  not  by  means  of  an  ocular, 
but  by  bringing  the  eye  directly  before  the  slit  o.  The  plane 


FIG.  2. 


ad,  which  is  the  hypotenuse  of  the  photometer  cube  W,  passes 
through  the  axis  of  the  instrument.  The  field  <?/;,  cd  is  lighted 
from  the  source  L' ',  and  the  field  be,  from  L. 

The  superiority  of  this  instrument  over  the  Vicrordt  and 
other  similar  spectral  photometers,  lies  in  the  greater  accuracy 
of  the  photometric  comparisons.  The  fields  to  be  compared  are 
not  separated  by  a  dark  band,  but  the  boundary  is  absolutely 
sharp,  and  disappears  altogether  when  equal  intensity  is  obtained. 
The  instrument  allows  not  only  this  principle  of  likeness,  but  the 
principle  of  contrast1  as  well.  Concerning  this  latter  method  it 

1  Zeitsch  rift  fiir  Instrument  >iki<  n</<-,  February  1892, 


SPECTRAL  PHOTOMETRIC  STUDIES  5 

may  be  remarked,  that  the  deviations  in  the  results  obtained 
by  it  are  only  one-eighth  as  great  as  in  those  obtained  by  the 
ordinary  photometers. 

In  order  to  test  the  law  of  proportionality  by  means  of  the 
variable  slit,  each  collimator  of  the  spectral  photometer  was 
provided  with  bilateral  slits.  Only  the  one  on  C'  was  used  for 
a  comparison  slit,  as  the  weakening  of  the  light  from  Zwas  done 
by  means  of  a  rotating  sector  placed  before  the  collimator  C. 
According  to  the  careful  measurements  made  by  Lummer  and 
Brodhun  with  the  rotating  sector  of  the  Physikalische  Tech- 
nischen  Reichsanstalt,  this  method  of  measuring  the  increase  or 
decrease  of  light  intensity  is  accurate  to  a  small  fraction  of  I 
per  cent. 

The  sector  was  driven  by  means  of  a  small  electric  motor, 
and  when  rotated  at  a  sufficient  speed  the  field  was  perfectly 
clear  and  free  from  flickering ;  any  increase  in  the  speed 
beyond  a  certain  limit  gave  no  change  whatever  in  the  results. 
During  the  investigations  the  sector  openings  were  each  set 
at  90°,  so  that  while  in  rotation  the  light  was  decreased  one- 
half. 

Various  kinds  of  light  sources  were  tried,  but  all  except  the 
incandescent  electric  lamp  were  either  too  weak  or  too  incon- 
stant to  give  satisfactory  results.  The  lamps  used  had  an  intensity 
of  about  50  candle  power  each,  and  were  connected  in  series  on 
the  circuit  of  a  storage  battery.  In  order  that  the  illumination 
of  the  two  slits  might  be  the  same  in  all  parts  they  were  covered 
with  milk  glass  plates.  The  plane  of  the  lamp  fiber  was  in  each 
case  parallel  to  the  glass  plates,  and  the  two  fibers  were  at  equal 
distances  from  the  center  of  the  collimator  slit. 

The  positions  of  the  lamps  were  made  secure  by  their  being 
firmly  fastened  to  T  shaped  bars,  which  were  screwed  to  the  base 
of  the  spectral  photometer. 

Before  beginning  the  investigation  some  preliminary  experi- 
ments were  made  to  determine  if  the  milk  glass  plates  were 
homogeneous  for  the  entire  area  to  be  used.  To  this  end  the 
slits  of  the  collimators  were  made  of  equal  widths,  but  both 


6  /).  it'.  MURruv 

quite  narrow.  With  equal  intensity  of  fields  established  in  this 
way  the  plates  were  moved  so  that  the  different  parts  were 
brought  over  the  slit.  No  change  due  to  this  movement,  how- 
ever, could  be  observed,  and  the  plates  were  considered  homo- 
geneous in  so  far  as  their  power  of  transmission  was  concerned. 
There  was  still  one  other  possible  source  of  error  that  must  be 
investigated.  The  two  lamp  fibers  were  not  at  equal  distances 
from  all  parts  of  the  glass  plates,  and  it  was  necessary  to  know 
whether  this  change  in  distance  affected  the  uniformity  of  the 
illumination  for  areas  as  great  as  were  to  be  used.  Computations 
on  this  showed  that  for  areas  icm  wide  the  variation  was  not 
greater  than  I  per  cent.  As  the  areas  to  be  used  were  but 
little  greater  than  imm  wide  any  error  due  to  this  cause  was 
negligible. 

The  slit  was  also  subjected  to  a  special  test,  and  by  means  of  a 
micrometer  microscope  its  widths  for  different  readings  of  the 
slit's  micrometer  screw  were  noted.  To  avoid  dead  motion  in 
the  screw  it  was  always  turned  in  the  same  direction  in  making 
the  settings  for  photometric  equality.  From  readings  on  the 
width  of  the  slit  up  to  2cm  the  reading  of  its  zero  point  was 
computed ;  this  was  to  avoid  any  change  due  to  tension  which 
might  be  brought  in  were  the  slit  to  be  entirely  closed. 

The  method  of  taking  the  readings  was,  in  principle,  very 
simple.  The  two  collimator  slits  were  set  at  the  same  widths 
and  the  lamps  adjusted  until  photometric  equality  was  roughly 
obtained.  The  exact  adjustment  was  then  made  by  means  of 
the  slit  of  C' .  A  series  of  readings  on  the  width  of  this  slit  for 
equal  intensities  of  fields  was  then  taken.  This  was  for  the 
total  light  from  L.  The  sector  was  next  started,  and  a  second 
series  of  readings  on  the  slit,  for  equal  intensities,  was  taken. 
The  light  from  Zwas  in  this  case  of  one-half  its  former  intensity. 
To  check  any  error  due  to  a  change  in  the  relative  intensities  of 
the  two  sources  the  sector  was  stopped  and  a  second  scries  of 
readings  for  the  total  light  from  L  was  taken. 

In  this  way  measurements  were  made  for  the  different  colors. 
The  position  of  the  observing  telescope  for  any  desired  color 


SPECTRAL  J'HOTOMETRIC  STUDIES 


was  found  by  means  of  a  mirror  attached  to  the  axis  on  which 
the  telescope  turned.  This  mirror  reflected  the  image  of  a  fixed 
scale,  whose  readings  for  the  different  wave-lengths  had  been 
previously  determined. 

Four  independent  series  of  measurements  for  the  entire 
length  of  the  spectrum  were  made.  The  widths  of  the  slit  ranged 
from  approximately  O.mm5  to  i.mm25. 

When  the  principle  of  likeness  in  the  photometer  was  used, 
the  mean  of  ten  readings  on  the  width  of  the  slit  was  taken. 
With  the  contrast  principle  the  agreement  was  so  very  close  that 
the  number  was  reduced  to  five. 

Results. — The  numerical  results  are  given  in  Tables  I  to  IV 
inclusive.  The  wave-length  of  the  light  used  is  given  in  col- 
umn I.  g  is  the  slit  width  without  the  sector,  and  2  b  is 
twice  the  slit  width  when  the  sector  was  used.  These  values 
are  in  terms  of  the  divisions  of  the  drum  of  the  micrometer 
screw  (80  div  =  imm).  S  is  the  percentage  of  difference  between 
g  and  2  b. 

TABLE  I. 


A 

f 

•zb 

8 

A 

f 

»S 

8 

480 

52.6 

53-4 

-1-5 

60O 

53-5 

51.8 

+3-3 

500 

54-o 

53-6 

+0.7 

620 

52.8 

5i.4 

+2.7 

520 

54-2 

53-6 

+1.1 

640 

52.9 

5i-4 

+  2.9 

54° 

54-5 

52.4 

+4-0 

660 

52.6 

51-8 

+  1-5 

560 

54-4 

52.8 

+3-0 

680 

51-7 

52.8 

—2.1 

580 

53-9 

52-4 

+  2.8 

TABLE  II. 


A 

g 

•2b 

8 

A 

g 

23 

s 

470 

56-3 

56.8 

—0.9 

610 

63.3 

6l.4 

+3.0 

490 

60.6 

60.2 

+0.6 

630 

63.4 

61.6 

+2.8 

510 

60.3 

59-2 

+  1.8 

650 

63-9 

62.4 

+  2-5 

530 

61.1 

59-6 

+2.5 

670 

64.1 

64.2 

—  0.2 

550 

61.9 

60.4 

+2.5 

690 

64.4 

65-2 

—  1.2 

570 

62.2 

61.2 

+  1.6 

700 

64-3 

65-4 

—  1-7 

590 

63-1 

60.8 

+3-8 

D.   W.  MURPHY 
TABLE  III. 


A 

g 

•  4 

a 

A 

g 

»i 

« 

480 

68.1 

68.6 

—0.7 

600 

72.9 

70.6 

+  3-3 

500 

69.7 

69.2 

+0.7 

620 

73-o 

71.0 

+  2.8 

530 

70.3 

69.4 

+1.3 

640 

73-5 

71.0 

+3-0 

540 

70.8 

69.2 

+2.3 

660 

74-4 

73-2 

+  1-4 

.  56o 

71.7 

69.8 

+2.7 

680 

75-3 

77.2 

—2-5 

58o 

72-5 

70.8 

+2.4 

700 

74.8 

79.2 

—5-5 

TABLE  IV. 


A 

g 

zb 

I 

A 

g 

*b 

& 

480 

98.5 

99.4 

—0.9 

600 

103.3 

101.8 

+  1-5 

490 

IOI.I 

102.0 

—1.9 

610 

103.3 

101.4 

+  1.9 

500 

100.8 

103.4 

—2-5 

620 

103.3 

1  01.  8 

+  1-5 

510 

98.4 

100.8 

—2.4 

630 

103.2 

102.0 

+1-3 

520 

98.8 

99.8 

—  I.O 

640 

104.3 

103.2 

+  I.I 

530 

99-7 

99-8 

—  O.I 

650 

102.9 

104.2 

—  1.2 

540 

100.2 

99.6 

-1-0.6 

660 

102.3 

105-8 

—2.4 

550 

100.6 

100.6 

±0.0 

670 

102.8 

107.2 

4-1 

560 

IOI.I 

1008 

-0.3 

680 

103.2 

109.0 

—5-3 

570 

101.8 

100.6 

-1.2 

690 

103.9 

I  12.0 

—7.2 

580 

102.2 

IOI.O 

-1.2 

700 

104.3 

II4.2 

-8.7 

590 

102.9 

101.6 

-i-3 

These  results  show,  for  the  light  source  used,  that  in  the 
middle  part  of  the  spectrum  the  increase  of  the  spectrum  inten- 
sity is  less  than  the  increase  in  the  slit  width,  that  is,  g—  2  b  >  0. 
At  the  ends  of  the  spectrum  just  the  opposite  is  observed.  These 
results  agree  with  those  deduced  from  a  consideration  of  the 
form  of  the  intensity  curve.  The  amounts  of  the  deviations  are 
different  for  the  different  wave-lengths,  and,  in  general,  are 
smaller  for  blue  than  for  green,  yellow,  and  extreme  red.  It  is 
further  shown,  that  for  a  given  wave-length  the  deviation  changes 
with  the  size  of  the  slit  used. 

Heretofore  the  measurc'ments  have  been  made  through  the 
entire  length  of  the  spectrum  with  nearly  the  same  width  of  slit, 
and  each  particular  series  gave  the  results  for  that  width  of  slit 
only.  In  order  to  study  more  fully  the  change  for  varying  slit 
widths  the  experiments  were  repeated  in  another  form.  Particu- 


SPECTRAL  PHOTOMETRIC  STUDIES 


9 


lar  colors  were  examined  for  different  slits,  from  the  smallest  to 
the  largest  size  with  which  the  measurements  were  possible.  In 
this  manner  results  were  obtained  for  the  wave-lengths  540, 
590,  and  690  />t/Lt.  In  Tables  V  to  VII,  inclusive,  the  results  are 
shown.  In  these  results  g,  b,  and  8  have  the  same  significance 
as  in  the  results  previously  given. 

TABLE  V.     (X= 


& 

*b 

8 

£ 

•zb 

S 

13.0 

14.4 

-9.8 

68.t 

67.0 

+  I-.7 

17.7 

19.0 

-6.8 

82.7 

81.6 

+  1-4 

27.7 

28.2 

-1.8 

103-3 

101.6 

+  1-7 

38.0 

37-8 

+0.5 

123.4 

122.0 

+  1.2 

53-2 

52.0 

+2.3 

I43-I 

140.0 

+2.2 

TABLE  VI.      \  = 


g 

•zb  • 

& 

f 

*b 

a 

13-1 

14.4 

—9.0 

68.5 

67.0 

+2.2 

1  8.0 

19.0 

—5-3 

84-3 

82.0 

+2-9 

27-9 

28.6 

—2.4 

104.3 

101.8 

+2-5 

38.6 

38.0 

+1.6 

124.0 

I20.O 

+3-6 

53-8 

52.2 

+3-1 

145-9 

I40.I 

+4.1 

TABLE  VII.     (X  =± 


g 

•2b 

B 

g 

•2l> 

1 

13-3 

14.6 

—9.0 

69.4 

70.2 

—  I.I 

18.1 

19.2 

—6.0 

86.7 

88.4 

—  1.9 

28.5 

29.0 

—1-7 

107.2 

1  10.2 

—2.7 

38.4 

38.8 

—  i.o 

126.6 

135-0 

—6.2 

54-4 

54-6 

—0.4 

147.8 

159.6 

—7.4 

These  tables  show,  in  the  first  place,  a  concordance  with  the 
former  ones ;  at  least  they  lead  to  the  same  general  conclu- 
sions. Beyond  this  they  teach,  that  for  slit  widths  below  a 
certain  value,  for  every  wave-length  g—2  b  becomes  <Co  ;  that  is, 
the  intensity  decreases  more  rapidly  than  the  width  of  the  slit. 


10  D.   W.  MURPHY 

The  reason  for  this  is  most  probably  the  loss  of  light  by  dif- 
fraction which  occurs  with  narrow  slits,  and  which  causes  a  loss 
of  light  proportionally  greater  as  the  slit  becomes  narrower. 

With  such  narrow  slits  the  accurate  determination  of  the 
zero  point  is  a  matter  of  much  importance,  and  no  doubt  small 
inaccuracies  arise  from  this  source.  It  is  not  probable,  how- 
ever, that  with  the  method  used  for  the  determination  of  the 
zero  point  the  error  is  sufficient  to  change  the  general  conclu- 
sions to  be  deduced. 

The  results  do  not  give  any  general  law  as  to  the  limit  of 
exactness  to  be  obtained  by  the  Vierordt  method  of  measuring 
the  light  intensity.  In  fact  any  general  law  is  impossible,  since 
it  varies  with  the  relative  intensities  and  the  kind  of  lamps  to 
be  compared. 

We  may  conclude,  however,  that  the  assumption  that  the 
spectrum  intensity  is  proportioned  to  the  width  of  the  slit  is 
not  strictly  true,  and  it  is  to  be  used  with  caution ;  that  in 
the  blue  and  central  parts  of  the  spectrum  it  is  in  error  for  slits 
in  the  ratio  of  I  to  2  as  much  as  2  or  3  per  cent.,  while  in  the 
red  this  error  may  become  as  great  as  10  per  cent.  This  shows 
that  this  method  of  measuring  light  intensity  is,  in  exactness, 
far  behind  the  present  methods  of  photometric  comparisons,  at 
least  with  such  an  instrument  as  the  Lummer-Brodhun  spectral- 
photometer.  This  apparatus  gives  with  the  intensity  of  light 
used  an  exactness  of  adjustment  of  about  0.3  per  cent.  Also 
by  means  of  the  rotating  sector  the  same  accuracy  for  decreas- 
ing the  light  is  obtained,  even  when  the  sector  openings  are 
small. 

INVESTIGATION  OF  THE  TRUTH  OF  THE  FRESNEL  FORMl'l  \  !<>K 
THE  INTENSITY  OF  REFLECTED  LIGHT,  AND  THE  DEPENDENCE 
OF  THIS  INTENSITY  ON  THE  COLOR  OF  THE  LIGHT  USED. 

Since  Fresnel,  from  a  theoretical  consideration,  gave  his 
celebrated  formula  for  the  amount  of  light  reflected  from  the 
surface  of  a  transparent  medium,  the  experimental  verification 
of  it  has  been  a  problem  of  interest  to  investigators  in  optical 


SPECTRAL  PHOTOMETRIC  STUDIES  I  I 

science.  And  of  all  the  methods  used,  the  photometer  —  the 
simplest  in  principle  —  was  applied  relatively  very  late.  This  is 
probably  due  in  a  large  degree  to  the  hitherto  inexactness  of 
photometric  measurements  which,  with  the  small  amount  of 
light  reflected,  gave  rise  to  serious  errors. 

It  is  for  this  reason  that  Professor  Rood,1  who  was  the  first 
to  investigate  the  subject,  prefers  measuring  the  amount  of  light 
transmitted  by  thin  plates  of  glass,  and  from  these  results  to 
compute  the  reflection  at  the  first  surface.  Lord  Rayleigh,2and 
shortly  after  him  Sir  John  Conroy3  were  the  first  to  choose  the 
experimentally  difficult,  but  decidedly  less  objectionable,  method 
of  measuring  directly  the  amount  of  the  reflected  light.  In 
order  to  prevent  the  great  loss  of  light  by  diffusion  which  takes 
place  in  the  ordinary  photometers,  Rayleigh  dispensed  with  the 
use  of  diffusion  screens  and  used  only  direct  reflection  from  the 
light  source  to  the  eye.  He  observed  from  the  amount  of  light 
reflected  from  the  surface  of  glass  prisms  that  only  those  sur- 
faces which  had  been  freshly  polished  gave  results  consistent 
with  theory.  Conroy  measured  not  only  the  light  reflected,  but 
also  that  transmitted  by  glass  plates,  hoping  in  this  manner  to 
find  an  explanation  for  the  differences  which  so  often  exist 
between  observed  and  computed  results.  He  concluded  that 
the  amount  of  light  reflected  from  a  glass  surface  varies  with 
the  kind  of  polish  to  which  the  surface  has  been  treated. 

Even  though  a  sufficient  reason  for  taking  up  the  subject 
anew  might  be  found  in  the  variations  of  results  heretofore 
obtained,  I  had  still  another  purpose  in  so  doing.  Rayleigh  and 
Conroy  in  their  investigations  used  white  light,  and  as  a  basis 
for  their  calculations  used  the  refractive  index  of  the  color  of 
greatest  intensity.  They  further  used  ordinary  unpolarized 
light,  while  the  Fresnel  formula  is  deduced  from  a  consideration 
of  lights  polarized  in  and  perpendicular  to  the  plane  of  incidence. 
A  much  more  complete  test  of  the  formula  would,  therefore,  be 

1  American  Journal  oj  Science,  50,  I. 

*Proc.  A'.  Sot.,  41,  275. 

3/VhV.  Trans.,  Vol.  A  1889,  p.  245. 


12  D.    W.  MURPHY  . 

obtained  by  working  with  light  polarized  at  different  angles  to 
the  plane  of  incidence.  So  far  as  I  know,  no  investigations  had 
been  made  on  the  amount  of  the  reflection  for  lights  of  differ- 
ent colors,  and  no  experiments  that  have  been  carried  on  in  a 
purely  photometric  way,  show  that  the  amount  of  reflection  is 
different  for  the  different  wave-lengths  of  the  light  used.1  By 
means  of  the  linear  bolometer,  Rubens  has  investigated  the 
Fresnel  formula  in  the  ultra-red  part  of  the  spectrum,  and  has 
found  that  the  amount  of  energy  reflection  varies  for  different 
wave-lengths. 

In  the  following  I  shall  show,  that  with  the  aid  of  the  Lum- 
mer-Brodhun  spectral  photometer,  in  connection  with  a  rotating 
sector  for  measuring  the  weakening  of  the  light,  and  a  second- 
ary spectrometer  for  determining  the  angle  of  incidence  of  the 
reflected  ray,  we  can  measure  the  amount  of  reflection  for  any 
wave-length  and  for  any  desired  angle  of  incidence.  By  using 
a  Nicol  placed  in  the  path  of  the  ray  it  is  possible  to  extend 
those  measurements  to  light  polarized  in  .any  desired  plane. 
The  measurements  to  be  made  with  special  care,  however,  are 
those  which  show  the  relations  of  the  intensities  of  the  different 
colors  in  the  spectra  of  the  direct  and  reflected  light. 

Method  of  investigation  and  description  of  the  apparatus.  —  In 
Fig.  3  is  shown  a  horizontal  cross  section  of  the  apparatus  giving 
the  arrangement  of  the  different  parts.  The  spectral  photom- 
eter consists  of  the  tubes  C,  C  and  Tt  the  photometer  cube 
Wt  and  the  refracting  prism  P.  C  and  C'  are  the  collimators 

1  The  Fresnel  formula, 


nM*'+r)        tan*  (*• 

in  which  7r  is  the  amount  of  light  reflected,  I\  the  incident,  i  the  angle  of  incidence, 
and  r  the  angle  of  refraction.  This  formula  shows  that  as  n  (the  refractive  index) 
increases,  sin  (i  —  r)  becomes  larger,  and,  up  to  a  certain  point,  where  (i  -f-  r  ~  90°), 
sin  (/  -j-  r)  becomes  smaller.  The  same  is  true  of  the  second  term.  The  formula 
then  says  that  for  a  given  angle  of  incidence  the  amount  of  reflection  will  be  a  func^ 
tion  of  the  refractive  index,  and  if  this  index  be  increased  the  amount  of  reflection 
will  be  increased.  We  can  further  deduce,  that  since  the  change  in  the  amount  of 
reflection  is  a  transcendental  function,  it  will  be  different  for  different  :ingk-s  of  inci- 
dence. 


SPECTRAL  PHOTOMETRIC  STUDIES  \  3 

by  means  of  which  the  light  rays  from  the  sources  L  and  L'  are 
rendered  parallel  before  reaching  the  photometer  W.  T  is  the 
observing  telescope  and  is  provided  with  a  variable  ocular  slit 
o.  When  the  apparatus  is  in  adjustment  an  eye  placed  before  o 
sees  the  photometer  fields  lighted  from  the  illuminated  slits  s 
and  sr .  The  light  sources  used,  L  and  L' ,  consisted  of  incan- 
descent electric  lamps  of  approximately  fifty  candle  power  each. 
The  lamps  were  joined  in  series  to  a  circuit,  and  supplied  with  a 


SP- 


FJG.  3. 


current  from  a  storage  battery,  having  an  E.  M.  F.  of  thirty-two 
volts.  The  light  source  L  is  firmly  fastened  to  an  arm  of  the 
spectral  photometer,  and  always  lights  in  the  same  manner  the 
one  field  of  the  photometer  W.  The  other  light  source,  Lr ,  is 
mounted  upon  a  separate  piece  of  apparatus,  Sp.  This  appa- 
ratus, which  is  a  form  of  spectrometer,  consists  essentially  of 
the  circular  plate  M  to  which  are  fastened  the  arms  Q  and  R. 
The  plate  M,  whose  diameter  is  about  5Ocm,  is  turned  from  a 
heavy  slab  of  slate,  and  its  edge,  being  graduated,  serves  as  the 


14  D.    W.  MURTHY 

spectrometer  circle.  The  metal  arm  R,  which  carries  the  lamp 
L' ,  is  so  mounted  that  it  turns  about  an  axis  through  the  center 
of  M)  and  its  position  is  read  by  means  of  the  graduated  circle. 
The  arm  Q  is  firmly  fastened,  and  always  retains  the  same  posi- 
tion relative  to  the  spectrometer  disk.  The  lamp  L'  is  enclosed 
so  that  the  only  light  emitted  from  it  is  through  the  slit  z.  The 
slit  s  and  the  collimator  slit  s  are  covered  with  milk  glass  plates 
p  and/',  the  purpose  of  which  is  to  give  a  more  uniform  field 
than  could  be  got  from  the  lamp  direct.  The  lenses  a  and  b  are 
mounted  so  as  to  slide  along  the  arms  Q  and  R  in  the  path  of 
the  ray.  These  lenses  are  so  adjusted  that  the  light  from  z 
passes  in  parallel  rays  from  b  to  a,  and  is  brought  to  a  focus 
again  on  the  slit  s' . 

The  spectrometer  as  a  whole  is  so  placed  that  when  the  arm 
R  is  at  its  zero  position,  that  is,  making  an  angle  of  1 80°  with 
Q,  the  axis  of  the  spectrometer  cuts  the  straight  line  passing 
through  the  center  of  IV and  the  slits  s'  and  z.  The  pencil  of 
light  between  b  and  a  will  then  be  concentric  with  the  line  of 
collimation  of  C' ,  and  will  cut  the  spectrometer  axis  at  right 
angles.  When  viewed  with  an  ocular  placed  before  o  the  images 
of  s  and  s'  will  be  seen  to  exactly  coincide,  and  the  color  of  the 
two  fields  will,  with  this  adjustment,  be  the  same  for  all  positions 
of  the  observing  telescope.  In  order  to  compare  the  intensities 
of  light  of  any  desired  wave-length,  it  is  only  necessary  to  turn 
the  telescope  T  until  that  color  is  brought  into  view. 

The  surface  whose  reflecting  power  is  to  be  measured  is 
placed  upon  the  table  of  the  spectrometer  in  such  a  position 
that  it  lies  in  the  plane  passing  through  the  axis.  By  rotating 
the  table  the  reflected  light  may  be  made  to  fall  upon  sr  for  all 
positions  of  the  arm  R. 

In  order  to  compute  by  means  of  the  Fresnel  formula  the 
amount  of  the  reflected  light,  one  face  of  a  Steinhcil  prism  was 
used  as  a  reflecting  surface.  The  refractive  indices  of  the  prism 
for  the  desired  wave-lengths  had  been  carefully  measured. 

The  light  from  the  source  L  was  weakened  to  the  same  inten- 
sity as  that  of  the  reflected  portion  from  L'  by  means  of  a  rotating 


SPECTRAL  PHOTOMETRIC  STUDIES  I  5 

sector  5  placed  between  L  and  the  slit  s.  The  size  of  the  sector 
opening  could,  during  rotation,  be  changed  at  will  from  180°  to 
O°,  and  by  means  of  a  vernier  read  to  an  accuracy  of  O°.O2.  Upon 
the  arm  Q,  and  between  the  reflecting  surface  and  the  lens  a,  a 
Nicol  prism  N  could  be  mounted.  By  revolving  the  Nicol  in  its 
mountings  the  light  which  fell  upon  s'  could  be  polarized  at  any 
desired  angle  with  the  plane  of  incidence. 

Dependence  of  the  amount  of  reflection  on  the  wave-length. — The 
method  of  finding  the  variation  in  the  amount  of  reflection  for 
different  wave-lengths  was  as  follows:  The  relation  of  the  inten- 
sities of  the  light  sources  L  and  L'  for  two  colors,  first  for  the 
direct  and  then  for  the  reflected  light,  was  measured.  A  com- 
parison of  these  ratios  gave  the  excess  of  reflection  for  one  color 
over  that  of  the  other. 

The  method  of  observation  for  this  is  very  simple  in  form. 
First,  the  slits  s  and  s'  are  set  at  approximately  the  same 
widths.  With  the  arm  R  at  its  zero  position  and  the  sector  open 
to  nearly  180°,  the  lamps  are  adjusted  until  the  fields  are  of 
nearly  the  same  intensity  for  one  color ;  all  other  conditions 
remaining  the  same,  equal  intensities  are  obtained  by  opening  or 
closing  the  sector.  After  a  series  of  ten  settings  has  been  made, 
and  readings  on  the  size  of  the  sector  opening  taken,  the  observ- 
ing telescope  is  turned  so  as  to  observe  the  light  of  the  other 
wave-length,  and  a  second  series  of  sector  readings  for  equal 
intensities  of  this  color  is  taken. 

The    ratio    -y,   of  the   sector  readings   tor  the   two   colors, 

which  is  denoted  by  7d,  is  the  relation  of  the  intensities  of  these 
colors  in  the  spectrum  of  the  direct  light  from  L' .  This  rela- 
tion is  in  terms  of  the  spectrum  from  L,  which  may  be  con- 
sidered of  unit  intensity  for  every  wave-length. 

The  arm  R  is  next  moved  from  its  zero  position,  and  the 
reflecting  surface  placed  on  the  table  of  the  spectrometer.  In 
order  to  bring  the  photometer  fields  to  the  same  intensity  when 
using  only  the  reflected  portion  of  the  light  from  L1 ',  it  would 
require  a  very  considerable  diminution  of  the  sector.  Measure- 


16  D.    II'.  AWRI'HY 

ments  made  in  this  way  do  not  possess  the  highest  degree  of 
accuracy  on  account  of  the  smallness  of  the  sector  opening.  To 
avoid  this  source  of  inaccuracy  the  sector  was  left  at  its  original 
size,  and  the  light  source  L  removed  until  the  intensities  were 
approximately  equal. 

The  values  of  0K'  and  0\ '  for  the  reflected  ray  were  then 
obtained  in  the  same  manner  as  for  the  direct  ray.  The  quo- 

O  ' 
tient,  —^y,  is  denoted  by  7r.      Fr9m  a  consideration  of  the  above 

we   have  —  as  the  relation  of  the  reflection  of  light  of  wave- 

Al 

length  \  to  that  of  light  of  wave-length  /. 

For  example,  the  readings  of  the  half-sector  openings  for 
wave-lengths  535/4/4  and  670/4/4,  for  the  direct  light  were  0*  = 
8i°.33  and  01  =  75°. 76  (^  being  considered  as  wave  535/4/4  and 
/  as  wave  670/4/4). 

The    value    of   7d    was    therefore    -  —^  =  1.074.     F°r    tne 

75-76 
light   reflected   at  incidence   angle   of  20°  the  results   obtained 

were  0K'  —  8o°.25  and  0\ '  —  73°. 35.  From  this  7r  =  1.094  and 
—-  =  1.019.  This  shows  that  for  light  of  wave-length  535/4/4, 

*d 

1.9  per  cent,  more  light  is  reflected  than  for  light  of  wave- 
length 670/^/4. 

TABLE  I. 

Relations  of  the  amounts  of  light  reflected  for  X=535/*Ai  and 


Incidence  angle 

Observed 

Computed 

20° 

I.OIQ 

I.OI5 

40 
60 

I.OI9 
I.OIO 

I.OI5 
1.008 

80 

1.003 

1.002 

The  results  of  these  investigations  for  different  incidence 
angles  are  given  in  Table  I.  The  computed  values  are  the  ratios 
of  the  amounts  of  reflection  taken  from  the  results  computed  by 
the  Fresnel  formula  for  the  corresponding  angle  of  incidence 


SPECTRAL  PHOTOMETRIC  STUDIES  17 

and  for  the  refractive  indices  of  the  glass  for  wave-lengths 
535/>t/Lt  and  bjo^p.  [See  Table  III.] 

Character  of  light  reflected  from  colored  plates. —  Measurements 
were  made  on  the  intensity  of  the  different  colors  of  the  spec- 
trum for  lights  reflected  from  different  colored  glass.  For  this 
purpose,  glass  plates,  the  reverse  side  of  which  had  been  cov- 
ered with  asphalt  black,  were  used.  Red,  as  well  as  blue, 
glasses  gave  for  the  blue  a  stronger  reflection  than  for  the  red 
rays,  showing  that  the  composition  of  the  reflected  light  is 
not  changed  by  the  color  of  the  reflecting  medium.  These 
results  were  not  compared  with  theory,  since  the  refractive 
indices  of  the  plates  for  different  wave-lengths  of  light  could 
not  be  readily  determined. 

Measurement  of  the  amount  of  light  reflected  for  different  colors 
and  at  different  angles  of  incidence. —  The  problem  of  measuring 
the  absolute  amount  of  light  reflected  is  in  theory  a  very  simple 
one.  For  its  solution  it  is  necessary  only  to  compare  the  total 
incident  light  from  L'  with  the  reflected  portion.  This  is  done 
by  taking  the  sector  readings  for  equal  intensities  of  the  photo- 
meter fields  with  R  at  its  zero  position  and  at  the  position  of  the 
desired  angle  of  incidence.  The  comparison  of  the  direct  with 
the  reflected  light,  however,  is  attended  with  two  experimental 
difficulties.  First,  the  reflected  portion  is  small,  being,  for  the 
smaller  angle  of  incidence,  only  about  4  per  cent,  of  the  total 
incident  light.  Second,  the  reflected  light,  more  especially  for 
large  angles  of  incidence,  is  partly  polarized  at  the  reflecting 
surface.  The  first  condition  leads  to  the  measuring  of  small 
sector  openings,  the  adjustment  and  reading  of  which  require 
especial  care  to  prevent  error. 

The  polarizing  of  the  light  at  the  reflecting  surface  may  lead 
to  another  source  of  error,  since  in  the  spectral  photometer  the 
refracting  prism  also  produces  polarization,  and  in  this  case  acts 
as  an  analyser  in  destroying  the  light  which  has  been  polarized 
by  reflection.  It  is  for  this  reason  that  photometers  consisting 
simply  of  diffusion  screens  have  in  some  cases  been  brought 
into  use  for  measuring  the  amount  of  reflected  light. 


t8  r>.  w. 

The  error  due  to  polarization  may,  however,  be  entirely 
avoided  by  placing  a  polarizer  in  the  path  of  the  ray,  between 
the  reflecting  surface  and  the  lens  a.  For  this  purpose  a  Nicol 
prism  of  45mmx45mm  opening  was  used.  With  this  arrangement 
the  measurements,  for  both  the  direct  and  the  reflected  rays,  are 
made  for  light  polarized  in  one  plane  whose  position  is  identical 
with  that  of  the  Nicol.  In  order  to  compare  the  results  obtained 
by  measurements  with  those  computed  from  the  formula  it  is 
necessary  to  know  accurately  the  polarizing  plane  of  the  Nicol. 
This  may  be  found  by  computing  from  the  refractive  index  with 
the  help  of  the  Brewster  formula,  ft=tan  ;,  the  angle  of  inci- 
dence under  which  the  reflected  light  is  totally  polarized.  The 
position  of  L'  is  adjusted  by  means  of  the  movable  arm  R  until 
the  light  falls  upon  the  surface  at  this  angle  ;  the  Nicol  is  then 
turned  until  the  light  which  reaches  the  photometer  from  L'  is 
a  minimum.  At  this  position  the  polarizing  plane  of  the  Nicol  is 
perpendicular  to  the  plane  of  incidence.  By  means  of  the 
graduated  circle  on  the  Nicol  mounting  I  was  able  to  bring  the 
polarizing  plane  to  any  desired  position  and  to  read  its  position 
to  an  accuracy  of  5'. 

Method  of  observation. — After  the  Nicol  had  been  adjusted 
the  reflecting  prism  was  removed  and  the  arm  A'  placed  at  its 
zero  position.  By  means  of  the  rotating  sector  the  photometer 
fields  were  brought  to  the  same  intensities,  and  a  series  of  five 
readings  on  the  size  of  the  sector  opening  was  taken.  The  arm 
was  then  turned  to  the  position  for  the  required  angle  of  inci- 
dence, and  the  prism  so  placed  that  the  reflected  light  fell  upon 
the  slit  s' .  Photometric  equality  was  then  brought  about  by 
closing  the  sector,  and  a  series  of  readings  on  the  size  of  the 
sector  opening  was  taken.  To  avoid  any  error  due  to  a  change 
in  the  relative  intensities  of  the  light  sources  during  the  measur- 
ing process,  the  arm  R  was  again  placed  in  its  zero  position,  the 
prism  removed,  and  a  second  scries  of  five  readings  of  the  sector 
for  direct  light  was  taken. 

The  ratio  of  the  two  sector  openings  gives  the  relation  of  the 
incident  to  the  reflected  light.  If  we  consider  the  incident  light 


SPECTRAL  PHOTOMETRIC  STUDIES 


equal  to  one  hundred,  which  has  been  done  in  the  following 
results,  the  amount  of  the  reflection  is  given  in  terms  of  per 
cent,  of  the  incident  light. 

Measurements  were  made  for  light  of  wave-lengths  535  A^ 
and  670  ft//-,  and  for  three  positions  of  the  polarizing  plane, 
which  were  at  angles  of  O°,  45°  and  90°  with  the  plane  of  inci- 
dence. 

The  results  are  given  in  the  following  tables.  /  is  the  angle 
at  which  the  incident  light  falls  upon  the  reflecting  surface. 
The  observed  values  are  the  results  obtained  from  a  single  series 
of  observations,  and  not  the  mean  of  several  sets  of  readings. 

The  computed  results  are  deduced  from  the  Fresnel  formula: 
L2(* —  r)          tan2(/- 
tan2  ( /  -f- 


T       


sin2  (/ +  r) 

The  refractive  indices  were  obtained  by  direct  measurement, 
and  were  for  wave-lengths  535  pp  and  670  ft/A  respectively, 
1.56462  and  1.55896. 

The  differences  between  the  observed  and  computed  results 
are  given  direct,  and  are  not  —  owing  to  the  different  values  of 
the  reflected  light — computed  in  terms  of  percentage. 

These  tables  show  in  general  a  close  agreement  between  the 
observed  and  computed  results,  the  differences  being  in  every 
case  but  a  small  percentage  of  the  total  incident  light,  while  in 
many  cases  they  are  almost  perfectly  concordant.  The  greatest 
discrepancy  exists  for  light  polarized  perpendicular  to  the  inci- 
dence plane,  and  in  this  case  for  the  small  angles  of  incidence. 

TABLE    II. 
Light  polarized  in  the  incidence  plane. 


\  =  670  fi/u. 

*  =  535  MM 

I 

Observed 

Computed 

5 

Observed 

Computed 

8 

20° 

5.60 

5-58 

-j-O.02 

5-61 

5.66 

—  0.05 

40 

9.24 

8.94 

+0.30 

9.20 

9.06 

—0.14 

60 

19.64 

19.64 

zhO.OO 

20.19 

19.80 

+  0.39 

80 

55-73 

56.04 

-0.3I 

56.72 

56.24 

-f0.48 

20 


/).    /K  MURrilY 


TAHLE  III. 
Light  polarized  at  an  angle  of  45°  to  the  incidence  plane. 


A  =  670  MM 

*  =  535  MM 

I 

Observed 

Computed 

£ 

Observed 

Computed 

& 

20° 

4.80 

4.80 

±:O.OO 

5.10 

4.87 

+0.23 

40 

5-60 

5-38 

-f-0.22 

5-63 

5.46 

+0.17 

60 

9.62 

9.87 

-0.25 

10.12 

9-95 

-0.17 

80 

39-07 

39-65 

—  0.56 

39-04 

39-73 

—  0.69 

TABLE    IV. 

Light  polarized  perpendicular  to  the  incidence  plane. 


A  =  670  MM 

*  =  535  MM 

' 

Observed 

Computed 

a 

Observed 

Computed 

a 

20° 
40 
60 

4-43 
2.03 

4.02 
1.82 
O  10 

+0.41 

-|-0.2I 

4-38 
2.00 

4.08 
1.86 
0  10 

+0.30 
-0.14 

80 

23-OS 

23.16 

—  O.I  I 

22.76 

23.22 

-0.46 

If  these  many  independent  observations  speak  for  the  cor- 
rectness of  the  Fresnel  formula,  they  also  give  evidence  of  the 
exactness  of  the  photometric  comparisons,  and  of  the  method  of 
measuring  by  means  of  the  rotating  sector  despite  the  small 
amount  of  reflected  light. 

As  the  measurements  for  light  polarized  perpendicular  to  the 
plane  of  incidence  could  not  be  repeated,  the  spectral  photom- 
eter being  in  use  for  other  investigations,  I  am  unable  to  give 
any  explanation  of  the  slightly  greater  variations  between 
observed  and  computed  results  in  this  particular  case.  It  is  not 
probable  that  the  Fresnel  formula  fails  to  give  correct  results  in 
this  particular  case,  but  that  the  cause  for  these  variations  is  to 
be  sought  for  in  some  other  source  of  inaccuracy. 

In  Table  V  I  have  given  the  results  obtained  without  using 
the  Nicol  at  Q;  this  will  show  the  magnitude  of  the  error  which 
may  affect  results  when  the  polarizer  is  not  used  as  a  ray  filter. 


SPECTRAL  PHOTOMETRIC  STUDIES 
TABLE  V. 


A  =  670    ft.fJL 

A  =  535  W 

I 

Observed 

Computed 

8 

Observed 

Computed 

8 

20° 

4.70 

4.80 

—  O.IO 

4-74 

4.87 

-0.13 

40 

4.60 

5-3« 

—  0.78 

4.62 

5-46 

—  0.84 

00 

7-77 

9.87 

—  2.IO 

7-79 

9-95 

—  2.16 

80 

34-44 

39.65 

-5-21 

34-41 

39-73 

-5-32 

The  calculated  values  for  the  reflection  of  ordinary  light  are 
the  same  as  for  light  polarized  at  an  angle  of  45°  to  the  inci- 
dence plane.  [Compare  Table  III.] 

For  small  angles  of  incidence  where  the  polarizing  effect  is 
small,  the  observed  and  computed  results  agree  to  within  2  per 
cent.  When  the  angles  of  incidence  are  large  this  difference 
rises  to  1 2  per  cent,  and  over. 

In  a  second  work,  which  I  hope  to  be  able  to  carry  out,  I 
shall  use  the  method  described  above  to  study  the  influence 
which  the  treatment  and  character  of  the  surface  have  on  the 
amount  of  the  reflected  light. 

In  conclusion  I  wish  to  express  my  thanks'  to  the  Physikalische 
Technischen  Reichsanstalt  for  the  opportunities  granted  me  for 
carrying  out  the  above  investigations,  and  to  the  members  of 
the  institution  for  the  many  courtesies  shown  me,  especially  to 
Professor  Lummer  and  Dr.  Brodhun,  to  whom  I  am  indebted 
for  much  valuable  assistance. 

STANFORD  UNIVERSITY, 
April  1897. 


507H-7,'16 


